This invention relates to band pass-band reject filters, in particular to a dual stage filter with feedback characterized by exceptional rejection of the fundamental frequency and minimal attenuation of its harmonics.
In the design of audio frequency distortion analyzers it is desirable to employ a band-reject, or "notch", filter that selectively removes the fundamental frequency component of a signal, allowing the amplitude of the residue to be measured. The amplitude of the residue relative to the amplitude of the signal prior to rejection of the fundamental component is a measure of the harmonic distortion in the signal. Ideally, the notch filter would totally reject frequencies within a predetermined bandwidth of the fundamental frequency without attenuating harmonics thereof. Conventional approaches, allowing for the aforementioned predetermined bandwidth, have resulted in filters exhibiting 0.2 to 0.5 dB attenuation at the second harmonic of the fundamental frequency.
One generally acceptable prior art type of band reject filter is a state variable notch filter which also produces a band pass output. An example of such a filter is shown in FIG. 1 hereof. LaPlace formulations of equations expressing the transfer functions for such a filter are as follows: ##EQU1## where R.sub.1, R.sub.2, and R.sub.3 are the values of the resistors shown in FIG. 1, .omega. is the fundamental frequency of the filter, and Q is the quality factor of the filter. .omega. and Q are determined as follows: ##EQU2## where R.sub.2, R.sub.3, R.sub.4, R.sub.5 and R.sub.6 are the values of respective resistors, R.sub.T is the value of both resistors R.sub.T1 and R.sub.T2, and C.sub.T is the value of both capacitors C.sub.T1 and C.sub.T2 shown in FIG. 1.
While such a circuit has useful applications, particularly since it provides both band reject and band pass outputs, it is inadequate as a notch filter in the measurement of extremely low levels of distortion, on the order of 0.001 percent, due to attenuation of harmonics of its fundamental frequency. This is so even where two such circuits are cascaded. Therefore, it would be desirable if an improved circuit were available that would allow exceptional rejection of a fundamental frequency in combination with minimal attenuation of its harmonics so as to permit measurements of distortion as low as 0.001 percent.